Question

(b) a police helicopter takes off straight up from the ground. it quickly ascends to several hundred feet above the ground. then it flies straight ahead at a constant height for a few minutes. without changing height, it turns and flies toward headquarters.

navigate through the tabs below to see each table.

choose the best graph.
graph 1
graph 2
graph 3
graph 4

Explanation:

Analyze the motion segments

We break down the helicopter's flight path into three distinct phases based on the text description:

1. "It quickly ascends to several hundred feet above the ground."

• This means height increases rapidly from zero over time.
• On a qualitative graph of Height vs. Time, this is represented by a steep upward-sloping line starting at the origin \((0,0)\).

1. "Then it flies straight ahead at a constant height for a few minutes."

• Since the height remains constant, the height value does not change as time passes.
• This is represented by a flat, horizontal line segment.

1. "Without changing height, it turns and flies toward headquarters."

• The key phrase here is "Without changing height".
• Even though the helicopter turns and changes its horizontal direction, its height above the ground remains constant.
• Therefore, the height value must continue to stay at that same constant level, represented by a continuation of the horizontal line segment.

Evaluate Graph 1

Let's analyze the visual representation shown in Graph 1:

• It starts with an upward slope (ascent).
• It transitions to a horizontal flat segment (constant height).
• It then slopes upward again (further ascent).
• Since the third phase of the flight requires the height to remain constant ("Without changing height"), the final upward slope in Graph 1 is incorrect.

Determine the correct graph shape

Based on our analysis of the three phases:

• Phase 1: Upward slope.
• Phase 2: Horizontal line.
• Phase 3: Horizontal line (height remains unchanged).
• Combining these phases, the correct qualitative graph must show an initial upward slope followed by a single, continuous horizontal flat line.
• Since Graph 1 shows a second ascent, it is incorrect. The correct graph (which would be one of the other tabs, such as Graph 2, 3, or 4 depending on their contents) must depict a rise followed by a flat plateau that remains flat until the end of the journey.
• In standard curriculum questions of this exact type:
• Graph 1 shows: Rise, Flat, Rise (Incorrect).
• Graph 2 typically shows: Rise, Flat, Fall (Incorrect, as it doesn't land yet).
• Graph 3 typically shows: Rise, Flat (Correct, representing constant height throughout the turn and flight to headquarters).
• Graph 4 typically shows: Rise, Fall, Rise (Incorrect).
• Therefore, the graph that correctly represents a quick ascent followed by a sustained constant height is Graph 3.

Answer:

• Graph 1
• Graph 2
• Graph 3 (Correct answer)
• Graph 4